Some sitcoms have themes that have changed (more than one song). Here is the list I came up with. Please add:

Ozzie & Harriet
I Dream of Jeannie
Bot Meets World
Eight is Enough
Flintstones
Frasier
Full House
Gilligan's Island
Gimme a Break
Happy Days
(Everybody Loves Raymond-symphonic version where they race to lock the
door)

Also, some show themes changed the lyrics:

Alice
Facts of Life
Mary Tyler Moore
(Gilligan-"the Professor and MaryAnn")

MASH (for the final couple episodes in the first season, it was played differently-and for some of the later shows)
Happy Days
Get Smart
Leave it to Beaver

Drew Carey Show had multiple theme songs.
The Munsters theme song was slightly different in the first season than in the second.
Silver Spoons and Small Wonder took their theme songs and spiced them up a little, so to speak. They went from sappy soft to quasi 80's rock. Same thing with Facts of Life.

Dallas changed their theme a little in the later shows.
The Bob Newhart show "jazzed up" their theme (called "Home to Emily") in, I think, their 3rd season (it was "jazzed up" by Bob James, who composed the theme for "Taxi")
Barreta had Sammy Davis record their theme for the 2nd season.
Bonnanza got a new theme, and opening, for the first-to-last season. But viewers complained, so for the last season, they brought back the "burning map" opening and the classic theme.

Roseanne added lyrics in the last (or last few) season(s).

THAT GIRL added lyrics to the theme in the last season.

Charles In Charge
Who's The Boss?

didn't batman have a slight change in the song for the episodes that batgirl was going to be in? I think they added a biff or bopp or something during the opening animation.

diff'rent strokes

Home Improvement had altered themes. Also, Mad About You for the last few seasons, and A Different World and The Cosby Show.

That '70s Show
8 Simple Rules (discontinued intro due to death of John Ritter)

The last season of Veronica Mars the theme song changed, it was like the same song, done differently.

Three's Company changed their song over the years too...like the same words, but sounded different.

Linda Lavin redid the Alice theme countless times throughout its run. The Barney Miller theme stayed basically the same, but it also had different variations. Same with the Little House on the Prairie theme.

"Perry Mason"had THREE different seasons,(first season,second through eighth season,and the final season-My favorite is the theme used in the second through eight seasons-"Gilligan's Island"had TWO(the first season was a light,tropical sounding theme,while the second season and third season had a theme that sounded like a military march),"Matlock"had TWO theme songs(the NBC theme,which I like FAR better,used in the NBC 1986-1992 episodes,and the ABC theme used in the ABC 1992-1996 episodes)

Oops! Sorry.I meant to say "Perry Mason"had THREE different themes,and TWO closing themes-FCirst season,and all other seasons.

MORK & MINDY changed their theme in the 2nd season to a "discoey-sounding" theme.

Starsky & Hutch changed themes as well - I think they had 3!!

Full House ( I know it was already said but, I'll explain. Season 2 used a lower octave in the singing, and music, and the music was more of a rock version as opposed to season 1. Season 3-5 was similar but the backround music was softer. Season 6 & 7 was like the 3-5 theme, but was shortened. And season 8 was even shorter.)

Family Matters ( Early season one's theme song was "What a Wonderful World". Late season 1 - season 3 used the song "As Days Go By", Seasons 4-6 was shorter, and seasons 7-9 didn't have a theme.)

Step by Step ( Season 1 was very long. Seasons 2 & 3 was shorter. Then seasons 4 & 5 was even shorter. Season 6 didn't have a theme. And season 7 returned the song but it was much shorter then the 4 & 5 theme)

Home Improvement ( All of the season basic changed the song, though it sounded similar. Season 1's version sounded different from the others. Season 2 & 3's version was a longer version, season 4-6's version was a shorter version from season 2 & 3. Season 7 & 8 sounded different too.)

Reba ( Season 1 was a country rock version. Seasons 2-4 used a saxaphone as it's main instrument, and the song was remixed. Seasons 5 & 6 used a gutair as it's main instrument, and the song was remixed again.)

What I Like About You ( Season 2-4's version was remixed from the season 1 version and the backround music was more of a rock version)

"Happy Days"had TWO themes(first was Bill Haley and the Comets'immortal "Rock around the Clock"(altered somewhat,and by that,I mean it did NOT include one verse .."When it's 8,9,10,11 too..I'll be going strong and so will you..")and the OTHER theme used in the third-final season.They also dropped the "Hello sunshine goodbye rain,she's wearing my schoolring on a chain.She's my steady,I'm her man,I'm gonna love her all I can..."verse from the closing